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4 years ago

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What are the coordinates of the image of point L(4, 2) after a reflection over the line y = –1?

1 answer:

andrey2020 [161]4 years ago

3 0

Answer:

L'(4, -4)

Step-by-step explanation:

When you're given a midpoint, you can find the point equidistant on the other side of the midpoint by subtracting the relevant coordinate from <em>double that of the midpoint</em>.

Here, the line of reflection is the horizontal line y=-1, so you know only the y-coordinate will change. The reflected point will be ...

(x, y) ⇒ (x, -2-y)

so the point of interest is ...

L' = (4, -2-2) = (4, -4)

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Kristen invests $ 5745 in a bank. The bank 6.5% interest compounded monthly. How long must she leave the money in the bank for i

podryga [215]

Answer:

1. 10.7 years

2. 17.0 years

3. 2nd option

Step-by-step explanation:

Use formula for compounded interest

$A=P\cdot \left(1+\dfrac{r}{n}\right)^{nt},$

where

A is final value, P is initial value, r is interest rate (as decimal), n is number of periods and t is number of years.

In your case,

1. P=$5745, A=2P=$11490, n=12 (compounded monthly), r=0.065 (6.5%) and t is unknown. Then

$11490=5745\cdot \left(1+\dfrac{0.065}{12}\right)^{12t},\\ \\2=(1.0054)^{12t},\\ \\12t=\log_{1.0054}2,\\ \\t=\dfrac{1}{12}\log_ {1.0054}2\approx 10.7\ years.$

2. P=$5745, A=3P=$17235, n=12 (compounded monthly), r=0.065 (6.5%) and t is unknown. Then

$17235=5745\cdot \left(1+\dfrac{0.065}{12}\right)^{12t},$

$3=(1.0054)^{12t},$

$12t=\log_{1.0054}3,$

$t=\dfrac{1}{12}\log_{1.0054}3\approx 17.0\ years.$

3. <u>1 choice:</u> P=$5745, n=12 (compounded monthly), r=0.065 (6.5%), t=5 years and A is unknown. Then

$A=5745\cdot \left(1+\dfrac{0.065}{12}\right)^{12\cdot 5},\\ \\A=5745\cdot (1.0054)^{60}\approx \$7936.39.$

<u>2 choice:</u> P=$5745, n=4 (compounded monthly), r=0.0675 (6.75%), t=5 years and A is unknown. Then

$A=5745\cdot \left(1+\dfrac{0.0675}{4}\right)^{4\cdot 5},\\ \\A=5745\cdot (1.0169)^{20}\approx \$8032.58.$

The best will be 2nd option, because $8032.58>$7936.39

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3 years ago

Read 2 more answers

X-5/2 =9 <br><br> solve for x

Liono4ka [1.6K]

Best Answer:<span> </span><span>(x - 5)^2 = 9
x - 5 = ±√9
x = 5 ± 3
x = 2, 8</span>

5 0

3 years ago

Read 2 more answers

Help please!!! Idk the answer.. if anyone knows then will u help me please!!! I will mark as BRAINLIEST

serious [3.7K]

Answer:

which one?

Step-by-step explanation:

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3 years ago

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Compute: (1 2/5 +3.5÷1 1/4 )÷2 2/5 +3.4÷2 1 /8 −0.35

nikdorinn [45]

Answer:

Answer: 3

Step-by-step explanation:

Use BODMAS

<u>Step 1: Open bracket (1 2/5 +3.5÷1 1/4 )</u>

<em>Convert mixed fractions into improper fractions</em>

7/5 + 3.5 ÷ 5/4

<em>Divide 3.5 by 5/4</em>

7/5 + 2.8 = 4.2

<u>Step 2: Carry out all divisions</u>

<em>Convert mixed fraction into improper fractions</em>

4.2 ÷2 2/5 +3.4÷2 1 /8 −0.35

4.2 ÷ 12/5 + 3.4 ÷ 17/8 - 0.35

1.75 + 1.6 - 0.35

<u>Step 3: Solve</u>

1.75 + 1.6 - 0.35

3.35 - 0.35

Answer = 3

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3 years ago

The value of √2+√2+2cos4x is?

Bogdan [553]

Answer:

2.82

Step-by-step explanation:

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